The original song comes from Lionel Monckton's "The Geisha Girl". The chorus was:

Chin Chin Chinaman, welly welly sad!
Me aflaid allee trade welly welly bad;
No-ee joke, blokee bloke, makee shutee shop;
Chin Chin Chinaman, chop chop chop.

One Glasgow playground version went:

Chin Chin Chinaman feeling very ill;
Walkee walkee down the street, buy a Beecham's pill;
Walkee walke home again, go to bed at night,
Wake up in the morning with his shirt all shite.